In the last couple of years, several approaches have been proposed, in order to address the impacts of the quantum geometry on the primordial power spectra. These include
the approaches of the deformed algebra [1]}, [2]}, [3]},
dressed metric [4]}, [5]}, [6]},
and hybrid [7]}, [8]}, [9]}, [10]}, [11]}
(For a recent discussion about similar ideas in anisotropic Bianchi I LQC spacetimes see Refs. [12]}, [13]}, [14]}, [15]} and references therein.). In particular, the last two approaches have been widely studied and found that they are all consistent with current cosmological observations [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}.
In addition, within the framework of the dressed metric approach recently it has been also shown that some anomalies from the CMB data [30]}, [31]}, [32]} can be
reconciled purely due to the quantum geometric effects [33]}, [34]}.
